The convergence of harmonic reduction to an internal sphere     

Arne Bjerhammar  Leif Svensson 《Journal of Geodesy》1979,53(3):247-257

The boundary value problem of physical geodesy has been solved with the use of a harmonic reduction down to an internal sphere using a discrete procedure. (For gravity cf. Bjerhammar 1964 and for the potential cf. Bjerhammar 1968). This was a finite-dimensional approach mostly with one-to-one correspondence between observations and unknowns on the sphere. Earlier studies were made with the use of surface elements (on the sphere) with constantgravity. Integration over the surface elements was replaced by a discrete approach with the use of the distance to a point in the centre of the surface element. See Bjerhammar (1968) and (1969). This approach was later presented as a “reflexive prediction” technique for a weakly stationary stochastic process. Bjerhammar (1974, 1976). Krarup (1969) minimized the L²-norm of the potential on the internal sphere. It will here be proved that the two solutions are identical for a proper choice of the radii of the internal spheres. The proof is given for a spherical earth with selected choice of “carrier points”. The convergence problem is discussed. The L²-norm solution is found convergent for the fully harmonic case. Uniform convergence is obtained in the non-harmonic case with the use of the original procedure applied in accordance with the theorems of Keldych-Lavrentieff and Yamabe.  相似文献   

P,T paths of natural eclogites during metamorphism — a record of subduction     

Arne Rheim  David H. Green 《Lithos》1975,8(4):317-328

The distribution of iron and magnesium between coexisting garnet and clinopyroxene is expressed by the distribution coefficient K_D^ga-cpx. This coefficient has been experimentally determined as a function of temperature and pressure, and is used to determine the temperature of equilibration of natural eclogites.

The presence of relict zoning in both garnet and clinopyroxene in low to medium temperature eclogites permits evaluation of the P,T path followed by these rocks during prograde metamorphism.

The average P,T path for eclogites of blueschist terranes (type C eclogites) is suggested to be 40°C/Kb during prograde metamorphism. The Tasmanian eclogite (type B) records crystallization along a different P,T path (lower pressure at given temperature) from those of the type C eclogites. Eclogites from the migmatite-gneiss terrances of Poland and Norway do not preserve evidence of prograde metamorphism in mineral zoning but indicate higher temperatures at the metamorphic maximum; pressures were similar to those attained by type C eclogites.  相似文献   

Arsenic in marine organisms from West Greenland     

Arne Bohn 《Marine pollution bulletin》1975,6(6):87-89

Natural background levels of trace metals in marine organisms from a West Greenland inlet were studied during the summer of 1972 and 1973. Dry weight arsenic levels ranged from 11.1 to 307 ppm in fish fillets and from 7.6 to 512 ppm in fish livers. Prawns had arsenic levels ranging up to 80.2 ppm, contrasting with 6.0 ppm in planktonic copepods. The results suggest that in certain marine organisms organo-arsenics predominate and are less toxic than inorganic arsenic compounds.  相似文献   

Study of peristerites using transmission electron microscopy and energy dispersive X-ray analysis     

Arne Olsen 《Contributions to Mineralogy and Petrology》1975,51(4):297-302

Peristerite feldspars from Seiland in Norway have been studied by a combination of transmission electron microscopy and energy dispersive X-ray analysis. The different types of microtextures have been correlated with the local mean composition, and it is found that the miscibility gap between An₄ and An₁₇ extends into the ternary Or—Ab—An region. The orientation of the more common type of exsolution lamellae varies from (08¯1) to about (¯1, 21, ¯2) with increasing potassium content.  相似文献   

Experimental determination of the temperature and pressure dependence of the Fe-Mg partition coefficient for coexisting garnet and clinopyroxene     

Arne Råheim  David H. Green 《Contributions to Mineralogy and Petrology》1974,48(3):179-203

An experimental study initiated to calibrate the distribution coefficient \(K_D = \frac{{({\text{FeO}}/{\text{MgO}})_{{\text{ga}}} }}{{{\text{(FeO}}/{\text{MgO)}}_{{\text{cpx}}} }}\) in eclogites as a geothermometer has been done on (a) a mineral mis, (b) a glass of the typical tholeiite composition and (c) a series of glasses of tholeiite compositions with \(6.2 < \frac{{100{\text{Mg}}}}{{{\text{Mg}} + {\text{Fe}}^{ + + } }} < 93.\) The mineral mix was found to be unsuitable as reactant due to incomplete equilibration but the minimum K _D of the mineral mix and the K _D from glass of tholeiite composition are identical within experimental uncertainty. These data constitute a reversal of the garnet/clinopyroxene partition relationship and provide justification of the use of glass as a reactant for the project. To eliminate any uncertainty in interpretation of mineral analyses due to possible variation in Fe⁺⁺⁺/Fe⁺⁺ between runs, experiments were carried out in iron capsules on the nine tholeiite glasses, thus maintaining iron as Fe⁺⁺. Microprobe analytical techniques yielded mineral analyses of comparable accuracy to analyses of natural phases for experiments within the temperature range from 600° C to 1500° C and a pressure range from 20 kb to 40 kb. It has been shown that for \(6.2 < \frac{{100{\text{Mg}}}}{{{\text{Mg}} + {\text{Fe}}^{ + + } }} < 85\) , the bulk chemical composition does not perceptibly affect the K _D value. At 30 kb the K _D value ranges from 18.0 at 600° C to 1.45 at 1400° C, defining the linear relationship in a ln K _D vs 1/T(°K) plot. The pressure dependence of the K _D -value has been shown to be greater than previously predicted. There is a straight line relationship in ln K _D vs Pressure (Kb) between 20 and 40 kb at constant temperature (1100°C). This enables us to determine K _D =fn (T, P) and \(T(^\circ {\text{K}}) = \frac{{3686 + 28.35 \times P({\text{Kb}})}}{{\ln K_D + 2.33}}\) . This expression uniquely determines the temperature of equilibration of natural eclogites of basaltic bulk composition when the K _D ^ga,cpx is known and a pressure estimate can be given.  相似文献   

Isometric anomaly     

Arne Bjerhammar 《Studia Geophysica et Geodaetica》1970,14(2):272-272

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On the geodetic boundary value problem for a fixed boundary surface—A satellite approach     

Arne Bjerhammar  Leif Svensson 《Journal of Geodesy》1983,57(1-4):382-393

Employing satellite-geometrical methods, the physical surface of the earth may be assumed to be known, while gravity measurements yield thelength of the gravity vector (including contributions from rotation). The problem then is to determine gravitational potential from such gravity observations. The corresponding linearized problem is an oblique derivative problem. The problem was discussed by Almqvist (1959), Koch (1970, 1971) and Koch and Pope (1972). Our presentation gives proofs for the existence (and uniqueness) of the solution in the non-linear case. The general implicit function theorem (in Banach spaces) is used to provewellposedness at least when data are close to given standard values (closeness is defined either in terms of Hölder or Sobolev norms). Iterative methods for solution by linear operators are given. The linearized problem is solved by harmonic reduction to an internal sphere in a generalization of the method by the first author for the Stokes problem. Also deflections of the vertical are treated.  相似文献   

Erratum to “Room-temperature magnetic properties of ferrihydrite: A potential magnetic remanence carrier?”[Earth Planet. Sci. Lett. 236 (2005) 856-870]     

Johari Pannalal  Maria T. Cioppa  Arne Sturm  David A. Fowle 《Earth and Planetary Science Letters》2005,240(2):537

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Growth of Barents Sea capelin (Mallotus villosus) in relation to zooplankton abundance     

Gjosaeter  Harald; Dalpadado  Padmini; Hassel  Arne 《ICES Journal of Marine Science》2002,59(5):959-967

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Airborne geophysical prospecting for ultramafite associated talc, Altermark, northern Norway     

Tor Arne Karlsen  Odleiv Olesen 《Journal of Applied Geophysics》1996,35(4):215-236

Talc-rich rocks in Altermark occur as rims around magnetite bearing serpentinite lenses which are up to about 1 km wide. The content of magnetite in the serpentinite makes magnetic measurements possible as a method for talc-prospecting. In 1991 a helicopter-borne geophysical survey combined with geological and petrophysical mapping was carried out in the Altermark area. Several positive magnetic anomalies were detected. Positive magnetic anomalies with oval shapes, well defined boundaries and smooth anomaly curves were interpreted to be caused by serpentinite lenses. Laboratory measurements revealed susceptibilities for the serpentinites between 0.006−0.36 SI and a Q-value of approximately 0.3. Magnetic modelling of the Nakkan anomaly and subsequent drilling revealed that it was indeed a serpentinite body surrounded by talc rocks which was the cause of the anomaly. The shallowest part was located about 150 m below surface. The geophysical exploration led to the discovery of a talc-carbonate deposit with an anticipated in situ tonnage of more than 1 million tons. The present study consequently proved to be a classical case study where we were able to locate and establish the three-dimensional form of serpentinite bodies associated with talc deposits. We conclude that helicopter-borne geophysical surveying is an effective tool in the exploration of serpentinite cored talc bearing rocks in complex geological areas where exposures are poor or absent and accessibility difficult. The rough topography and dense vegetation in the Altermark area make this type of survey very cost effective.  相似文献